Abstract
AbstractThe purpose of this note is to show that a finitely generated graded module M over $$S=k[x_1,\ldots ,x_n]$$
S
=
k
[
x
1
,
…
,
x
n
]
, k a field, is sequentially Cohen-Macaulay if and only if its arithmetic degree $${\text {adeg}}(M)$$
adeg
(
M
)
agrees with $${\text {adeg}}(F/{\text {gin}}_\textrm{revlex}(U))$$
adeg
(
F
/
gin
revlex
(
U
)
)
, where F is a graded free S-module and $$M \cong F/U$$
M
≅
F
/
U
. This answers positively a conjecture of Lu and Yu from 2016.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Simons Foundation
Dipartimenti di Eccellenza
Publisher
Springer Science and Business Media LLC
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